Malliavin Calculus for Lévy Processes with Applications to Finance

By Giulia di Nunno, Bernt Øksendal, Frank Norbert Proske. 2008

475 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/00e9a81f13c0583fc6c9664207a47f5d0f19735e

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Citations in the corpus

Asymptotic independence of multiple Wiener-It\^o integrals and the resulting limit laws (2011, background): “1(t1,...,tq)f2(tq+1,...,t2q) ×f3(tσ(1),...,tσ(q))f4(tσ(q+1),...,tσ(2q))dµ(t1)...dµ(t2q) = 1 (2q)! Xq r=0 hf1 ⊗r f3,f4 ⊗r f2iCard{σ∈ S2q : {σ(1),...,σ(q)}∩ {1,...,q} = r}, from which we deduce (2.15). (3) We have (g⊗eg)(t1,...,t2q) = 1 (2q)! X σ∈S2q g(tσ(1),...,tσ(q))g(tσ(q+1),...,tσ(2q)) = 1 (2q)! X”
A PRIMAL–DUAL ALGORITHM FOR BSDES (2013, background): “The second term on the right-hand side has zero conditional expectation, because the Wick product interchanges with the conditional expectation, i.e., E [ Wt+ − Wt θt+ ∣∣∣∣FWt ] = E [ Wt+ − Wt ∣∣∣∣FWt ] E [θt+ |FWt ] = 0, see, e.g., lemma 6.20 in Di Nunno et al. (2009).”
Integration by parts formula and applications to equations with jumps (2009, background): “[6] much work concerning the Malliavin calculus for Poisson point measures has been done and many different approaches have been developed: see for example [1,8,13,19,21].”
Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation (2012, background): “See, for example, [20, 26] or [8] for more information about Malliavin calculus.”
On Malliavin's differentiability of BSDEs with time delayed generators driven by Brownian motions and Poisson random measures (2010, background): “It is possible to define Malliavin’s derivative for pure jump processes in such a way that it coincides with Picard’s difference operator, see [12].”
Strong Solutions of Mean-Field Stochastic Differential Equations with irregular drift (2018, methodology): “10, we can apply the duality formula [35][Corollary 4.”
Anticipating Random Periodic Solutions--I. SDEs with Multiplicative Linear Noise (2015, background): “(Skorohod integral [24]) Suppose that v(t, ω) is a stochastic process such that v(t, ·) is F-measurable and square-integrable for all t ∈ R.”
A variational approach to the construction and Malliavin differentiability of strong solutions of SDE’s (2013, background): “As for Malliavin calculus the reader is referred to 73 [30, 22, 23, 8].”
Malliavin Calculus in Lévy spaces and Applications to Finance. (2008, methodology): “These are extensions of the results in [4] and [10] from simple Poisson processes to square integrable Lévy processes.”